PC-lattices: A Class of Bounded BCK-algebras

• Autorzy: Sadegh Khosravi Shoar , Rajab Ali Borzooei , R. Moradian , Atefe Radfar
• Języki publikacji: EN

Abstrakty

EN

In this paper, we define the notion of PC-lattice, as a generalization of finite positive implicative BCK-algebras with condition (S) and bounded commutative BCK-algebras. We investiate some results for Pc-lattices being a new class of BCK-lattices. Specially, we prove that any Boolean lattice is a PC-lattice and we show that if X is a PC-lattice with condition S, then X is an involutory BCK-algebra if and only if X is a commutative BCK-algebra. Finally, we prove that any PC-lattice with condition (S) is a distributive BCK-algebra.  

Słowa kluczowe

EN

PC-lattice; BCK-lattice; Involutory BCK-algebras; Bounded commutative BCK-algebras

• Wydawca: Wydawnictwo Uniwersytetu Łódzkiego
• Czasopismo: Bulletin of the Section of Logic
• Rocznik: 2018
• Tom: 47
• Numer: 1

Daty

wydano

2018-03-30

Twórcy

autor

Sadegh Khosravi Shoar

• Department of Mathematics, Fasa University, Fasa, Iran

autor

Rajab Ali Borzooei

• Department of Mathematics, Shahid Beheshti University, Tehran, Iran

autor

R. Moradian

• Department of mathematics Farhangian University, Tehran, Iran

autor

Atefe Radfar

• Payame Noor University, p. o. box. 19395-3697, Tehran, Iran

Bibliografia

• [1] C. Bărbăcioru, Positive implicative BCK-algebras, Mathematica Japonica 36 (1967), pp. 11–59.
• [2] R. A. Borzooei, S. Khosravi Shoar, Implication Algebras are Equivalent to the Dual Implicative BCK-algebras, Scientiae Mathematicae Japonicae 633 (2006), pp. 429–431.
• [3] R. A. Borzooei, S. Khosravi Shoar, R. Ameri, Some new filters in MTL-algebras, Fuzzy Sets and Systems 187(1) (2012), pp. 92–102.
• [4] B. A. Davey, H. A. Priestley, Introduction to Lattices and Order, Cambridge University Press, 1990, 2002.
• [5] G. Grätzer, General Lattice Theory, Academic Press, 1978.
• [6] Y. Huang, BCI-algebras, Science Press, 2006.
• [7] Y. Huang, On involutory BCK-algebras, Soochow Journal of Mathematics 32(1) (2006), pp. 51–57.
• [8] Y. Imai, K. Iséki, On axioms systems of propositional calculi XIV, Proceedings of the Japan Academy 42 (1966), pp. 19–22.
• [9] K. Iséki, BCK-algebras with condition (S), Mathematica Japonica 24 (1979), pp. 107–119.
• [10] K. lséki, On positive implicative BCK-algebras with condition (S), Mathematica Japonica 24 (1979), pp. 107–119.
• [11] K. Iséki and S. Tanaka, An introduction to the theory of BCK-algebras, Mathematica Japonica 23 (1978), pp. 1–26.
• [12] J. Meng and Y. B. Jun, BCK-Algebras, Kyung Moon Sa Co, Seoul, Korea, 1994.
• [13] S. Tanaka, A new class of algebras, Mathematics Seminar Notes 3 (1975), pp. 37–43.
• [14] S. Tanaka, On ^-commutative algebras, Mathematics Seminar Notes 3 (1975), pp. 59–64.

Identyfikatory

DOI

10.18778/0138-0680.47.1.03